.. _V2.02.140:

**v2.02.140** SDLL140 — Calculation of the natural modes of a beam with 3 disks, subject to the gyroscopic effect.
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**Summary:**

This problem consists in validating the effect of the gyroscopic matrix on a beam supported at each of its ends, on linear supports. The beam is solid, has a circular cross section and has three disks.

Two calculations are carried out:


* Calculation A: zero rotation speed, no gyroscopic effect, calculation of natural frequencies,


* Calculation B: non-zero rotation speed, presence of gyroscopic effect, calculation of natural frequencies,

This problem therefore makes it possible to test the effect of the gyroscopic matrix that was developed for a straight beam. The gyroscopic effect leads to the duplication of modes. The evolution of natural frequencies as a function of the speed of rotation makes it possible to build the Campbell diagram.

The results obtained are in good agreement with those given in reference. The references are based on Timoshenko's beam theory.


.. toctree::
    :hidden:

    self

.. toctree::
    :maxdepth: 2
    :numbered:

    Probl_me_de_r_f_rence
    Solution_de_r_f_rence
    Mod_lisation_A
    R_sultats
    Synth_se_des_r_sultats